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After fitting an ARIMA model with a covariate using the auto.arima function in R, I get the following results enter image description here

What could be the reason as to why my results do not include the intercept. Also, I would highly appreciate interpreting the important metrics from the summary above.

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The function auto.arima() has many arguments that you can add. Maybe what you are looking for auto.arima(x, allowmean = TRUE), because I am not sure that the default settings allows mean to be modeled. Also, as @Stephan-Kolassa said, apparently no mean is needed.

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